Second part
As to the most recent specific prophecies from the living prophet Thomas S. Monson so far I have come up with this:
There remain, however, areas of the world where our influence is limited and where we are not allowed to share the gospel freely. As did President Spencer W. Kimball over 32 years ago, I urge you to pray for the opening of those areas, that we might share with them the joy of the gospel. As we prayed then in response to President Kimball’s pleadings, we saw miracles unfold as country after country, formerly closed to the Church, was opened. Such will transpire again as we pray with faith. Thomas S Monson, President of the Church, October 2008
The fall of Communism in Europe was what opened up those countries. It to me therefore seems that President Monson was prophesying the current unrest in the dictatorships throughout the world and that this will eventually allow for LDS missionaries to enter some of those countries. As the missionaries are not currently in any of the countries (nor is the unrest overwith) this is one that we should be able to watch develop.
Plus the prophecy that there will be more temples built. Further revelation given is such things as the calling of a new apostle, the calling of missionaries, and other adminstrative things which while important to the Church I doubt anyone outside of the Church cares (excluding some ex-mormons (along with some social mormons that don't understand the doctrine) that are really upset over Prop. 8 and the reaffirming the Churches stance against homosexual behaviors, which they really should have known anyways).
I have previously listed some of the other prophecies that have come true as well as some other prophecies that to me seem very specific. I can try finding more but in the end it will almost always be possible to say that "my idol did it" or anyone could have known that or "Some things they may have guessed right, among so many; but behold, we know that all these great and marvelous works cannot come to pass, of which has been spoken" or other such things. I am very much of the opinion that signs, prophecies, and miracles will not and should not provide sufficient evidence to convince someone without they themselves asking God to know if it is true. They should, however, provide evidence enough to begin to act and to be willing to test things out.
I do know of another precedure that is empirical but it is asking a lot more of people. Also, I am not asking for donations to my church, as I explain:
Malachi 3:10: "Bring ye all the tithes into the storehouse ... and prove me now herewith, saith the Lord of hosts, if I will not open you the windows of heaven, and pour you out a blessing, that there shall not be room enough to recieve it". Here is what I am actually suggesting, find some organization or charity that you beleive to be good and give that organization 10% of your income (measured however you think is honest with yourself) track your expenditures, your income, and net worth over the course of a year and then at the end of the year of so doing evaluate your situation, see if God followed through on His promise. If you believe that SIAI is a good organization then donate to them. I don't care who you donate it to as long as you believe it to be a good worthwhile cause, therefore if you don't think my church is true then please don't donate to it, as I doubt it will be effective if you do.
You should look at information gain when evaulating the strength of a prophecy. For instance, "closed countries will become open at some point in the future." Assume this requires a major change in government, then look at the expected rate of major government change--I'm going to make a guess of a 2% chance per year. After 14 years (1976-1990), observing a government change major enough to open a country gives you around 2 bits of information.
That means this "prophecy" is approximately as impressive as prophecying correctly that a fa...
(Disclaimer: This post is sympathetic to a certain subset of theists. I am not myself a theist, nor have I ever been one. I do not intend to justify all varieties of theism, nor do I intend to justify much in the way of common theistic behavior.)
I'm not adopted. You all believe me, right? How do you think I came by this information, that you're confident in my statement? The obvious and correct answer is that my parents told me so1. Why do I believe them? Well, they would be in a position to know the answer, and they have been generally honest and sincere in their statements to me. A false belief on the subject could be hazardous to me, if I report inaccurate family history to physicians, and I believe that my parents have my safety in mind. I know of the existence of adopted people; the possibility isn't completely absent from my mind - but I believe quite confidently that I am not among those people, because my parents say otherwise.
Now let's consider another example. I have a friend who plans to name her first daughter Wednesday. Wednesday will also not be adopted, but that isn't the part of the example that is important: Wednesday will grow up in Provo, Utah, in a Mormon family in a Mormon community with Mormon friends, classmates, and neighbors, attending an LDS church every week and reading scripture and participating in church activities. It is overwhelmingly likely that she will believe the doctrines of the LDS church, because not only her parents, but virtually everyone she knows will reinforce these beliefs in her. Given the particular nuances of Mormonism as opposed to other forms of Christianity, Wednesday will also be regularly informed that several of these people are in a position to have special knowledge on the subject via direct prayer-derived evidence2 - in much the same way that her parents will have special knowledge of her non-adopted status via direct experience when she wasn't in a state suitable to notice or remember the events. Also, a false belief on the subject could have all kinds of bad consequences - if the Muslims are right, for instance, no doubt Hell awaits Wednesday and her family - so if she also correctly assumes that her parents have her best interests at heart, she'll assume they would do their best to give her accurate information.
Atheism tends to be treated as an open-and-shut case here and in other intellectually sophisticated venues, but is that fair? What about Wednesday? What would have to happen to her to get her to give up those beliefs? Well, for starters, she'd have to dramatically change her opinion of her family. Her parents care enough about honesty that they are already planning not to deceive her about Santa Claus - should she believe that they're liars? They're both college-educated, clever people, who read a lot and think carefully about (some) things - should she believe that they're fools? They've traveled around the world and have friends like me who are, vocally, non-Mormons and even non-Christians - should she believe that her parents have not been exposed to other ideas?
Would giving up her religion help Wednesday win? I don't think her family would outright reject her for it, but it would definitely strain those valued relationships, and some of the aforementioned friends, classmates, and neighbors would certainly react badly. It doesn't seem that it would make her any richer, happier, more successful - especially if she carries on living in Utah3. (I reject out of hand the idea that she should deconvert in the closet and systematically lie to everyone she knows.) It would make her right. And that would be all it would do - if she were lucky.
Is it really essential that, as a community, we exclude or dismiss or reflexively criticize theists who are good at partitioning, who like and are good at rational reasoning in every other sphere - and who just have higher priorities than being right? I have priorities that I'd probably put ahead of being right, too; I'm just not in a position where I really have to choose between "keeping my friends and being right", "feeling at home and being right", "eating this week and being right". That's my luck, not my cleverness, at work.
When Wednesday has been born and has learned to read, it would be nice if there were a place for her here.
1I have other evidence - I have inherited some physical characteristics from my parents and have seen my birth certificate - but the point is that this is something I would take their word for even if I didn't take after them very strongly and had never seen the documentation.
2Mormons believe in direct revelation, and they also believe that priesthood authorities are entitled to receive revelations for those over whom they have said authority (e.g. fathers for their children, husbands for their wives, etc.).
3I have lived in Salt Lake City, and during this time was, as always, openly an atheist. Everyone was tolerant of me, but I do not think it improved my situation in any way.